Why does the Torah switch from "Aharon" to 'ha'Kohen asher Yimshach oso ... "?
Rashi and Rashbam: Since throughout the Parshah, the Torah referred exclusively to Aharon, the Torah found it necessary to explain that the same applies to the Kohanim Gedolim who serve after him. 1
Kol Eliyahu, Divrei Eliyahu: Vayikra Rabah (21:7) says that Aharon was permitted to enter the Kodesh ha'Kodoshim on any day 2 , with the Korbanos mentioned here. Until now, the Torah discussed this. Now it teaches that every Yom Kipur, the Kohen Gadol has a Mitzvah to enter with these Korbanos.
Why does the Torah add "va'asher Yemalei es Yado ... "?
Rashi and Seforno: To include a Kohen Gadol who is initiated by wearing the eight Begadim, and was not anointed with Shemen ha'Mishchah. 1
During the era of the second Beis-ha'Mikdash, when the Shemen ha'Mishchah was not available.
What are the implications of "Lechahein Tachas Aviv"?
Rashi: This teaches us that if the Kohen Gadol's son is worthy to succeed his father, he has priority over all other contenders. 1
Moshav Zekenim: Similarly, the head of Kalah (a gathering to learn the laws of the festival before the festival), if his son is worthy to succeed him, he has priority.
What is the Pasuk referring to when it writes that Aharon did everything that Hashem commanded Moshe?
Rashi #1: The Pasuk is teaching us that Aharon did everything mentioned above when Yom Kipur arrived.
Rashi #2: It means that Aharon wore the Bigdei Kehunah, not because of the Kavod that they afforded him, but in order to carry out the command of Hashem.
Ramban: It also teaches us that Aharon was careful never to enter the Kodesh Kodashim except on Yom Kipur with the prescribed Korbanos.